A Forming Limit Diagram (FLD) is a graph which depicts the major strains versus values of the minor strains at the onset of localized necking. Experimental determination of a FLD is usually very time consuming and requires special equipment. Many analytical and numerical models have been developed to overcome these difficulties. The Gurson- Tvergaard- Needlemann (GTN) damage model is a micromechanical model for ductile fracture. This model describes the damage evolution in the microstructure with physical equations, so that crack initiation due to mechanical loading can be predicted. In this work by using the GTN damage model, a failure criterion based on void evolution was examined. The aim is to derive constitutive equations from Gurson's plastic potential function in order to predict the plastic deformation and failure of sheet metals. These equations have been solved by analytical approach. The Forming Limit Diagrams of some alloys which studied in the literatures have been predicted using MATLAB software. The results of analytical approach have been compared with experimental and numerical results of some other researchers and showed good agreement. The effects of GTN model parameters including 〖 f〗_0 〖,f〗_C 〖,f〗_N,f_f , as well as anisotropy coefficient and strain hardening exponent on the FLD and the growth procedure of void volume fraction have been investigated analytically.